proc_values: Recover private costs from procurement (lowest-bid-wins)...

In qdfauction: Nonparametric Quantile Density Estimation and Structural Analysis of First-Price Auctions

Recover private costs from procurement (lowest-bid-wins) auctions

Description

Reflects the bids, b' = M - b, calls fpa_values on the reflected sample, and maps the result back: costs c = M - v', ranks u = 1 - u', quantile density q(u) = q'(1-u). This implements c = b - (1-\eta)(1-u)q(u)/(n-1) under independence and the copula analogue otherwise.

Usage

proc_values(bids, n = NULL, M = NULL, monotone = "isotonic", ...)

Arguments

bids	L \times n matrix of bids (one row per auction), or a vector with n given.
n	Number of bidders; taken from ncol(bids) for a matrix.
M	Reflection constant; default proc_M(bids).
monotone	Monotonisation of the pseudo-values; "isotonic" by default, because the spline replacement extrapolates into the lower (winning) tail of procurement bids.
...	Passed to fpa_values (method, bandwidth, family, theta, eta, ...). family must be "independence", "frank" or "nonparametric".

Value

An object of class "proc_values": bids (ascending), u, q, psi, markup (b - c), costs_raw, costs, costs_mat (for matrix input), M, n, and reflected, the fpa_values fit on M - b used by the cost functionals.

qdfauction documentation built on Nov. 10, 2026, 5:07 p.m.